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Question 2

The electrostatic force on a small sphere of charge 0.4 μC due to another small sphere of charge − 0.8 μC in air is 0.2 N.

(a) What is the distance between the two spheres?

(b) What is the force on the second sphere due to the first?

Answer

 (a) Electrostatic force on the first sphere, F = 0.2 N

Charge on this sphere, q1 = 0.4 μC = 0.4 × 10−6 C

Charge on the second sphere, q= − 0.8 μC = − 0.8 × 10−6 C

Electrostatic force between the spheres is given by the relation,

F space equals space fraction numerator q subscript 1 q subscript 2 over denominator 4 straight pi element of subscript 0 straight r squared end fraction space
A n d comma space fraction numerator 1 over denominator 4 straight pi element of subscript 0 end fraction space equals space 9 space cross times space 10 to the power of 9 space N space m squared space C to the power of minus 2 end exponent

Where, ∈0 = Permittivity of free space

r squared space equals space fraction numerator q subscript 1 q subscript 2 over denominator 4 straight pi element of subscript 0 straight F end fraction
space space space space equals fraction numerator 0.4 space cross times 10 to the power of minus 6 end exponent space cross times 8 space cross times 10 to the power of minus 6 end exponent space cross times 9 space cross times 10 to the power of 9 over denominator 0.2 end fraction
space space space space equals space 144 space cross times space 10 to the power of minus 4 end exponent
r space equals space square root of 144 space cross times 10 to the power of minus 4 end exponent end root
space space space equals.12 space m space

The distance between the two spheres is 0.12 m.

(b) Both the spheres attract each other with the same force. Therefore, the force on the second sphere due to the first is 0.2 N.

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